Finite Group Databasebeta

← C4×#15689027 #26137477

Subgroups — C4×#15689027 #26137477

Order 12032.

2110 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic94C211yesmaximal, characteristic
2C2×#15689027C212yesmaximal
3C2×C4×Dic47⋊C4C211yesmaximal, characteristic
4C2×C42×Dic47C211yesmaximal, characteristic
5#20241622C212yesmaximal
6#20241619C212yesmaximal
7Dic47⋊#95C212yesmaximal
8C4×C47⋊#95C211yesmaximal, characteristic
9C4×C47⋊#95C211yesmaximal, characteristic
10C4×C47⋊#95C211yesmaximal, characteristic
11C4×#95×C47C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×C4×Dic94—24no—
14C2×C4×Dic94—24no—
15C2×C4×Dic94C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2212yes—
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2212yes—
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2212yes—
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15689027C4116yesdirect product factor
27C4×Dic47⋊C4—24no—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C42×Dic47—24no—
36C22×C42×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C2×#95×C47C2212yes—
40C2×#95×C47C2212yes—
41C22×Dic94—22no—
42C22×Dic94—22no—
43C22×Dic94—24no—
44C22×Dic94C2×C418yes—
45C22×Dic94C2×C414yes—
46C23×Dic47C2312yes—
47C23×Dic47C2311yescharacteristic
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2312yes—
51C23×Dic47C2311yescharacteristic
52C4×Dic94—232no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47C2×C414yes—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4C2×C418yes—
63C2×Dic47⋊C4C2×C414yes—
64C2×Dic47⋊C4C2×C414yes—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—22no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—24no—
69C2×C4×Dic47—22no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—24no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—24no—
74C2×C4×Dic47—22no—
75C2×C4×Dic47—22no—
76C2×C4×Dic47—22no—
77C2×C4×Dic47C2×C418yes—
78C2×C4×Dic47C2×C414yes—
79C2×C4×Dic47C2×C414yes—
80C2×C4×Dic47D414yes—
81C2×C4×Dic47D414yes—
82C2×C4×Dic47Q814yescomplemented
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C47⋊#95C2×C418yes—
88C47⋊#95C2×C418yes—
89C47⋊#95C2×C418yes—
90C23×C4×C47C2312yes—
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2312yes—
94C23×C4×C47C2311yescharacteristic
95C2×C42×C47—22no—
96C2×C42×C47—22no—
97C2×C42×C47—22no—
98C2×C42×C47—22no—
99C2×C42×C47—22no—
100C2×C42×C47—22no—
101C2×C42×C47—22no—
102C2×C42×C47C2×C414yes—
103C2×C42×C47Q814yescomplemented
104#95×C47—24no—
105#95×C47C2×C418yes—
106C24×C47C2411yescharacteristic
107C22×C4×C47—22no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C22×C414yes—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C22×C414yes—
128C22×C4×C47C22×C414yes—
129C22×C4×C47C22×C412yes—
130C22×C4×C47C2×D412yes—
131C22×C4×C47C2×D412yes—
132C22×C4×C47C2×Q814yes—
133C22×C4×C47C2×Q812yes—
134C22×C4×C47C2×Q812yes—
135C22×C4×C47#4114yes—
136C22×C4×C47#4112yes—
137C22×C4×C47#4112yes—
138C22×Dic47—22no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47C22×C414yes—
158C22×Dic47C22×C412yes—
159C22×Dic47C22×C414yes—
160C22×Dic47C22×C412yes—
161C22×Dic47C22×C412yes—
162C22×Dic47C22×C414yes—
163C22×Dic47C22×C412yes—
164C22×Dic47C22×C414yes—
165C22×Dic47C2×D412yes—
166C22×Dic47C2×D412yes—
167C22×Dic47C2×D412yes—
168C22×Dic47C2×D412yes—
169C22×Dic47C2×Q814yes—
170C22×Dic47#4114yes—
171C22×Dic47#4114yes—
172C2×Dic94—28no—
173C2×Dic94—28no—
174C2×Dic94—216no—
175C2×Dic94—216no—
176C2×Dic94C42116yescomplemented
177C42×C47—28no—
178C42×C47—28no—
179C42×C47—44no—
180C4⋊Dic47—28no—
181Dic47⋊C4—28no—
182Dic47⋊C4—28no—
183Dic47⋊C4—216no—
184C4×Dic47—216no—
185C4×Dic47—28no—
186C4×Dic47—28no—
187C4×Dic47—216no—
188C4×Dic47—44no—
189C4×Dic47C22⋊C4116yes—
190C23×C47C23×C411yescharacteristic
191C23×C47C23×C412yes—
192C23×C47C22×D411yescharacteristic
193C23×C47C22×D411yescharacteristic
194C23×C47C22×Q811yescharacteristic
195C23×C47C22×Q811yescharacteristic
196C23×C47C2×#4112yes—
197C23×C47C2×#4112yes—
198C23×C47C2×#4111yescharacteristic
199C23×C47C2×#4111yescharacteristic
200C23×C47C2×#4112yes—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—24no—
206C2×C4×C47—24no—
207C2×C4×C47—24no—
208C2×C4×C47—24no—
209C2×C4×C47—24no—
210C2×C4×C47—24no—
211C2×C4×C47—22no—
212C2×C4×C47—24no—
213C2×C4×C47—24no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—24no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47C2×C4214yes—
224C2×C4×C47C2×C22⋊C414yes—
225C2×C4×C47C4×Q814yes—
226C2×C4×C47C4×Q814yes—
227C2×C4×C47C4×Q818yescomplemented
228C2×C4×C47C22⋊Q814yes—
229C2×C4×C47C22⋊Q814yes—
230C2×C4×C47#12414yes—
231C2×C4×C47C4⋊Q814yes—
232C2×Dic47—22no—
233C2×Dic47—22no—
234C2×Dic47—24no—
235C2×Dic47—24no—
236C2×Dic47—24no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—24no—
240C2×Dic47—24no—
241C2×Dic47—24no—
242C2×Dic47—24no—
243C2×Dic47—24no—
244C2×Dic47—24no—
245C2×Dic47—24no—
246C2×Dic47—22no—
247C2×Dic47—24no—
248C2×Dic47—24no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—24no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47C2×C4214yes—
259C2×Dic47C2×C4214yes—
260C2×Dic47C2×C22⋊C414yes—
261C2×Dic47C2×C22⋊C414yes—
262C2×Dic47#11714yes—
263C2×Dic47C4×D418yes—
264C2×Dic47C4×D418yes—
265C2×Dic47C4×Q818yescomplemented
266Dic94—232no—
267C4×#391—471nomaximal, Sylow
268C22×C47C22×C4211yescharacteristic
269C22×C47C22×C22⋊C411yescharacteristic
270C22×C47C2×#11711yescharacteristic
271C22×C47C2×C4×D412yes—
272C22×C47C2×C4×D412yes—
273C22×C47C2×C4×Q812yes—
274C22×C47C2×C4×Q811yescharacteristic
275C22×C47C2×C4×Q812yes—
276C22×C47C2×C4×Q811yescharacteristic
277C22×C47C4×#4112yes—
278C22×C47C4×#4111yescharacteristic
279C22×C47C4×#4111yescharacteristic
280C22×C47C4×#4112yes—
281C22×C47C2×C22⋊Q811yescharacteristic
282C22×C47C2×C22⋊Q811yescharacteristic
283C22×C47#52512yes—
284C22×C47C2×#12411yescharacteristic
285C22×C47#52912yes—
286C22×C47#52912yes—
287C22×C47C2×C4⋊Q811yescharacteristic
288C22×C47#53212yes—
289C22×C47#53312yes—
290C22×C47#53312yes—
291C4×C47—24no—
292C4×C47—28no—
293C4×C47—42no—
294C4×C47—44no—
295C4×C47#39118yescomplemented
296Dic47—24no—
297Dic47—24no—
298Dic47—28no—
299Dic47—42no—
300Dic47—44no—
301Dic47C4×C22⋊C418yes—
302C22×C4×Q8—471no—
303C2×#391—472no—
304C2×C4×C4⋊C4—471no—
305C2×C43—471no—
306#1436—472no—
307#1436—472no—
308C4⋊#95—472no—
309C4×#95—471no—
310C4×#95—471no—
311C4×#95—471no—
312C4×#95D4711yescharacteristic
313C2×C47C2×C4×C22⋊C411yescharacteristic
314C2×C47C42×Q811yescharacteristic
315C2×C47C42×Q811yescharacteristic
316C2×C47C2×#39111yescharacteristic
317C2×C47#229511yescharacteristic
318C2×C47#229511yescharacteristic
319C2×C47#229711yescharacteristic
320C2×C47C4×C22⋊Q812yes—
321C2×C47C4×C22⋊Q812yes—
322C2×C47C4×#12412yes—
323C2×C47C4×C4⋊Q812yes—
324C23×Q8—471no—
325C2×C4×Q8—478no—
326C2×C4×Q8—944no—
327C2×C4×Q8—944no—
328C22×C4⋊C4—471no—
329C22×C4⋊C4—471no—
330C22×C4⋊C4—471no—
331C22×C4⋊C4—472no—
332C22×C42—471no—
333C22×C42—472no—
334C22×C42—471no—
335C22×C42—471no—
336C22×C42—472no—
337C22×C42—471no—
338C22×C42C2×D4711yescharacteristic
339C22×C42C2×D4711yescharacteristic
340C22×C42C2×D4711yescharacteristic
341#391—4716no—
342C4×C4⋊C4—944no—
343C2×#95—472no—
344C2×#95—472no—
345C2×#95—472no—
346C2×#95—472no—
347C2×#95—472no—
348C2×#95—472no—
349C2×#95—472no—
350C2×#95C2×D4712yes—
351C2×#95C2×D4712yes—
352C43—944no—
353C47C4×#39111yescharacteristic, complemented, Sylow
354C22×Q8—474no—
355C22×Q8—478no—
356C22×Q8—942no—
357C22×Q8—942no—
358C22×Q8—944no—
359C23×C4—471no—
360C23×C4—471no—
361C23×C4—471no—
362C23×C4—472no—
363C23×C4—471no—
364C23×C4—472no—
365C23×C4C22×D4711yescharacteristic
366C23×C4C22×D4712yes—
367C23×C4C22×D4712yes—
368C23×C4C22×D4711yescharacteristic
369C23×C4C22×D4711yescharacteristic
370C4×Q8—9432no—
371C2×C4⋊C4—474no—
372C2×C4⋊C4—474no—
373C2×C4⋊C4—474no—
374C2×C4⋊C4—478no—
375C2×C4⋊C4—942no—
376C2×C4⋊C4—942no—
377C2×C4⋊C4—942no—
378C2×C4⋊C4—942no—
379C2×C4⋊C4—942no—
380C2×C4⋊C4—942no—
381C2×C4⋊C4—944no—
382C2×C4⋊C4—944no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—474no—
391C2×C42—474no—
392C2×C42—474no—
393C2×C42—474no—
394C2×C42—478no—
395C2×C42—474no—
396C2×C42—944no—
397C2×C42—944no—
398C2×C42—944no—
399C2×C42—944no—
400C2×C42—944no—
401C2×C42—942no—
402C2×C42—942no—
403C2×C42—942no—
404C2×C42—942no—
405C2×C42—942no—
406C2×C42—942no—
407C2×C42—942no—
408C2×C42Dic9414yescomplemented
409C2×C42C4×D4714yes—
410#95—24no—
411#95—478no—
412#95—478no—
413#95—478no—
414#95—944no—
415#95—944no—
416#95—944no—
417#95—944no—
418#95C4×D4718yes—
419C24C23×D4711yescharacteristic
420C2×Q8—4716no—
421C2×Q8—948no—
422C2×Q8—948no—
423C2×Q8—9416no—
424C2×Q8—9416no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—472no—
443C22×C4—474no—
444C22×C4—472no—
445C22×C4—472no—
446C22×C4—474no—
447C22×C4—474no—
448C22×C4—474no—
449C22×C4—472no—
450C22×C4—472no—
451C22×C4—472no—
452C22×C4—472no—
453C22×C4—474no—
454C22×C4—474no—
455C22×C4—474no—
456C22×C4—472no—
457C22×C4—942no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—941no—
468C22×C4—941no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4C2×Dic9414yes—
477C22×C4C2×Dic9412yes—
478C22×C4C2×C4×D4714yes—
479C22×C4C2×C4×D4712yes—
480C22×C4C2×C4×D4714yes—
481C22×C4C2×C4×D4712yes—
482C22×C4C2×C4×D4714yes—
483C22×C4C2×C4×D4712yes—
484C22×C4#1062535014yes—
485C22×C4#1062535012yes—
486C22×C4D4×D4712yes—
487C22×C4D4×D4712yes—
488C22×C4#1062535212yes—
489C22×C4Q8×D4712yes—
490C4⋊C4—9416no—
491C4⋊C4—948no—
492C4⋊C4—948no—
493C4⋊C4—948no—
494C42—28no—
495C42—28no—
496C42—44no—
497C42—4716no—
498C42—9416no—
499C42—9416no—
500C42—948no—
501C42—948no—
502C42—1884no—
503C23C22×C4×D4711yescharacteristic
504C23C22×C4×D4712yes—
505C23C2×D4×D4711yescharacteristic
506C23C2×D4×D4711yescharacteristic
507C23C2×Q8×D4711yescharacteristic
508C23C22×Dic9411yescharacteristic
509C23#41×D4712yes—
510C23#41×D4712yes—
511C23C2×#1062535211yescharacteristic
512C23C2×#1062535011yescharacteristic
513C23C2×#1062535012yes—
514Q8—9432no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—474no—
538C2×C4—474no—
539C2×C4—474no—
540C2×C4—478no—
541C2×C4—478no—
542C2×C4—474no—
543C2×C4—474no—
544C2×C4—478no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—944no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—944no—
553C2×C4—944no—
554C2×C4—944no—
555C2×C4—944no—
556C2×C4—944no—
557C2×C4—944no—
558C2×C4—944no—
559C2×C4—942no—
560C2×C4—944no—
561C2×C4—944no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—944no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4C42×D4714yes—
572C2×C4C22⋊C4×D4714yes—
573C2×C4#1309398914yes—
574C2×C4C4×Dic9414yes—
575C2×C4C4×Dic9418yescomplemented
576C2×C4#1309400114yes—
577C2×C4#1309400214yes—
578C2×C4#1309401014yes—
579C2×C4#1309402314yes—
580C22C2×C42×D4711yescharacteristic
581C22C2×C22⋊C4×D4711yescharacteristic
582C22#117×D4711yescharacteristic
583C22C4×D4×D4712yes—
584C22C4×D4×D4712yes—
585C22C4×Q8×D4712yes—
586C22C2×#1309398911yescharacteristic
587C22C2×C4×Dic9411yescharacteristic
588C22C2×C4×Dic9412yes—
589C22C4×#1062535212yes—
590C22#1568959111yescharacteristic
591C22C4×#1062535011yescharacteristic
592C22C4×#1062535012yes—
593C22C2×#1309400111yescharacteristic
594C22C2×#1309400211yescharacteristic
595C22#1568963212yes—
596C22C2×#1309401011yescharacteristic
597C22#1568965112yes—
598C22#1568965312yes—
599C22C2×#1309402311yescharacteristic
600C22#1568967012yes—
601C22#1568967612yes—
602C22#1568967712yes—
603C4—28no—
604C4—24no—
605C4—42no—
606C4—44no—
607C4—478no—
608C4—944no—
609C4—948no—
610C4—944no—
611C4—1882no—
612C4—1884no—
613C4#1568902718yesdirect product factor
614C2C4×C22⋊C4×D4711yescharacteristic
615C2C4×#1309398911yescharacteristic
616C2C42×Dic9411yescharacteristic
617C2C2×#1568902711yescharacteristic
618C2#2024586011yescharacteristic
619C2#2024586411yescharacteristic
620C2#2024587411yescharacteristic
621C2C4×#1309400112yes—
622C2C4×#1309400212yes—
623C2C4×#1309401012yes—
624C2C4×#1309402312yes—
subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC4×#95×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC4×#95D47
hypocenterC47C4×#391
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
15. C2×C4×Dic94C4semidirect
26. #15689027C4direct (N × H)
82. C2×C4×Dic47Q8semidirect
103. C2×C42×C47Q8semidirect
176. C2×Dic94C42semidirect
227. C2×C4×C47C4×Q8semidirect
265. C2×Dic47C4×Q8semidirect
295. C4×C47#391semidirect
353. C47C4×#391semidirect
408. C2×C42Dic94semidirect
575. C2×C4C4×Dic94semidirect
613. C4#15689027direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4×Dic942
C2×#156890272
C2×C4×Dic47⋊C42
C2×C42×Dic472
#202416222
#202416192
Dic47⋊#952
C4×C47⋊#952
C4×#95×C472
C4×#39147